Math Snap

STEP 1

Assumptions1. The function h(x) represents the state's income tax for a single person in a recent year, where x is the person's taxable income.
. The function is defined as a piecewise function with three different rules for different ranges of taxable income.
3. The function is defined as follows - If the taxable income x is between0 and5999 (inclusive of0 and exclusive of6000), the tax is% of the taxable income.
- If the taxable income x is between6000 and10999 (inclusive of6000 and exclusive of11000), the tax is $120 plus3$6000.
- If the taxable income x is $11000 or more, the tax is$270 plus4% of the amount by which the taxable income exceeds $11000.

STEP 2

First, we need to calculate the tax for a taxable income of $1260. Since$1260 falls in the first range (0 to5999), we use the first rule of the function.
$$h(1260) =0.02 \times1260$$

STEP 3

Calculate the tax amount for a taxable income of $1260.
h(1260) =0.02 \times1260 = \($\)25.2The tax for a taxable income of $1260 is$25.2.

STEP 4

Next, we need to calculate the tax for a taxable income of $7160. Since$7160 falls in the second range (6000 to10999), we use the second rule of the function.
$$h(7160) =120 +0.03 \times (7160 -6000)$$

STEP 5

Calculate the tax amount for a taxable income of $7160.
h(7160) =120 +0.03 \times (7160 -6000) = \($\)150 + \($\)348 = \($\)468The tax for a taxable income of $7160 is$468.

STEP 6

Finally, we need to calculate the tax for a taxable income of $49070. Since$49070 falls in the third range (11000 and above), we use the third rule of the function.
$$h(49070) =270 +0.04 \times (49070 -11000)$$

Calculate the tax amount for a taxable income of $49070.
h(49070) =270 +0.04 \times (49070 -11000) = \($\)270 + \($\)1522. = \($\)1792.The tax for a taxable income of $49070 is$1792..